Riemannian Cartan–Hadamard theorem
GPTKB entity
Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifolds
|
| gptkbp:field |
differential geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemannian Cartan–Hadamard theorem
|
| gptkbp:implies |
exponential map at any point is a covering map
universal covering space of such a manifold is contractible |
| gptkbp:namedAfter |
gptkb:Jacques_Hadamard
gptkb:Élie_Cartan |
| gptkbp:relatedTo |
gptkb:Cartan–Hadamard_conjecture
gptkb:Hadamard's_theorem |
| gptkbp:state |
A complete, simply connected Riemannian manifold with non-positive sectional curvature is diffeomorphic to Euclidean space
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|